Optimal Put Exercise: An Empirical Examination of Conditions for Mortgage Foreclosure

Implicit in option-pricing models of mortgage valuation are threshold levels of put-option value that must be crossed to induce borrower default. There has been little research into what these threshold values are that come out of pricing models or how they compare to exercised option values seen in empirical data. This study decomposes boundary conditions for optimal default exercise to look at the economic dynamics that should lead to optimal default timing. Empirical data on FHA insured mortgage foreclosures is then examined to discern the predictive influence of optimal-option-valuation-and-exercise variables on observed default timing and values. Interesting results include a new understanding of how to measure and use property equity variables during economic downturns, house-price index ranges over which default is exercised for various classes of borrowers, and implied differences in appreciation rates between market-price indices and foreclosed properties.     

Valuation of Residential Mortgage-Backed Securities with Default Risk Using an Intensity-Based Approach

This paper develops a valuation model for fixed-rate mortgages, mortgage pools, and residential mortgage-backed securities (RMBS's) using an intensity-based approach. This model incorporates full prepayment, partial prepayment, and default in valuing a mortgage. Full prepayment is further classified into “refinancing” and “sale of a house” depending on the reason. The time of occurrence of each of these three types of prepayment and default is modeled as the first jump time of a Cox process. Under these conditions, the valuation formula for a mortgage as well as a partial differential equation (PDE) that the mortgage value satisfies is provided. As for implementation of the model, the short-term riskless interest rate and the house price are adopted as state variables. Each intensity process is specified in a manner that allows a jump in intensity depending on the state variables and the borrower's incentive for prepayment or default. Through such specifications, it is shown that our model has characteristics similar to some structural models in previous literature. As for the numerical method for valuation, we propose a simple backward induction technique on a tree instead of the commonly used Monte Carlo method. Additionally, the method for estimating the model is discussed, and the results of numerical simulations are reported.This paper represents the view of the author and does note necessarily the views of the Mitsubishi UFJ Securities Co., Ltd. or members of its staff.     

交易所国债期限风险溢价的实证研究

本文考察了上海证券交易所国债期限风险溢价的时间变化特征及决定因素。实证结果显示，债券剩余期限越长，平均风险溢价越高；通过对不同期限债券组合的风险溢价序列建立回归模型，发现长短期利差及风险溢价的前期值对中长期债券期限风险溢价的时变性具有明显的解释能力。     

Embedded Options in the Mortgage Contract

Loss mitigation is the process by which lenders attempt to minimize losses associated with foreclosure. As competition increases in the mortgage industry, lenders and servicers are under great pressure to adopt loss mitigation tactics rather than simply use foreclosure as the means of dealing with borrowers in default. This study presents a mortgage-pricing model that fully specifies all borrower options with respect to default, including the ability to reinstate the mortgage out of default. We document the impact of various loss mitigation programs, including forbearance and antideficiency judgments, as well as the value of credit on borrower default behavior.     

Household Income, Termination Risk and Mortgage Pricing

The premium embedded in home mortgage loans to compensate investors for their exposure to prepayment risk is a significant component of the cost of home mortgage lending. Moreover, there is some reason to believe that prepayment risk may be lower for loans to lower-income housing borrowers, especially those that are first-time home owners. If so, investor recognition of this advantage should facilitate greater willingness to acquire portfolios of lower-income housing loans, and encourage more competitive pricing in this segment of the market. This study investigates the possibility of differential mortgage prepayment behavior between lower-income home owners and non-low income home owners. The investigation relies on samples of the American Housing Survey spanning ten years of experience from 1985 to 1995. We find no significant difference between the termination or refinancing behavior of non-low income and low-income households. This result is robust to a number of alternative specifications such as restricting the low-income test group to non-moving households and to first-time owners. The same conclusions are derived from both aggregate prepayment rates and from analysis of individual household prepayment behavior.     

Pricing the Credit Risk of Secured Debt and Financial Leasing

Abstract:  This paper presents closed form solutions to price secured bank loans and financial leases subject to default risk. Secured debt fair credit spreads always increase in the debtor's default probability, whereas financial leasing fair credit spreads may well decrease in the lessee's default probability and even be negative. The reason is that the lessor, unlike the secured lender, can gain from the lessee's default, especially when the leasing contract envisages initial prepayments or the lessee's terminal options to either purchase the leased asset or to extend the lease maturity. This result, which critically depends on contractual and bankruptcy code provisions, can explain some of the empirical evidence and the use of financial leases as an alternative to secured bank lending to finance small, risky and relatively opaque firms.     

The Effect of Mortgage Price and Default Risk on Mortgage Spreads

Variations over time in mortgage yield spreads should reflect changes in the underlying prepayment option value; moreover, the relationship between mortgage yield spreads and interest rate dynamics should weaken as the value of the borrowers prepayment option declines. We verify this hypothesis through an empirical analysis of residential mortgage yield spread behavior, and we also present evidence that the strength of the relationship between mortgage spreads and interest rate dynamics weakens (strengthens) as the level of default risk increases (decreases). This result is consistent with the competing risks effect between a borrowers option to prepay or default. Our results demonstrate the importance of accounting for mortgage price discount to par as well as default risk when developing time series of mortgage yields.     

An Empirical Comparison of Credit Spreads between the Bond Market and the Credit Default Swap Market

This paper compares the pricing of credit risk in the bond market and the fast-growing credit default swap (CDS) market. The cointegration test confirms that the theoretical parity relationship between the two credit spreads holds as a long-run equilibrium condition. Nevertheless, substantial deviation from the parity can arise in the short run. The panel data study and the VECM analysis both suggest that the deviation is largely due to the higher responsiveness of CDS premia to changes in credit conditions. Moreover, it exhibits a certain degree of persistence in that only 10% of price discrepancies can be removed within a business day.     

运用抵押率降低贷款行业风险

恰当地管理贷款行业中存在的风险至关重要。长期以来,放贷人借助首付准则和抵押贷款保险来降低风险敞口。本文讨论了抵押贷款行业中风险管理的各种方法,着重讨论了欧美的情况。     

住房贷款违约风险定量分析初探

本首先剖析了影响住房贷款违约风险的主要因素，然后引入Merton的结构化模型来分析住房贷款在等额偿还方式下违约风险的度量问题，并从横向和纵向两个角度，通过模拟计算得出房价波动率和无风险利率对住房贷款的违约概率、预期损失和违约风险溢价的影响规律以及这三个指标在贷款期内的变化规律。     

Default Risk, Asset Pricing, and Debt Control

The pricing and control of firms’ debt has become a majorissue since Merton’s (1974) seminal article. Yet Mertonas well as other recent theories presume that the asset valueof the firm is independent of the debt of the firm. However,when using debt finance, firms may have to pay a premium foran idiosyncratic default risk and may face debt constraints.We demonstrate that firm-specific debt constraints and endogenousrisk premia, based on collateralized borrowing, affect the assetvalue of the firm and, in turn, the collateral value of thefirm. In order to explore the interdependence of debt financeand asset pricing of firms, we endogenize default premia andborrowing constraints in a production-based asset pricing model.In this context then the dynamic decision problem of maximizingthe present value of the firm faces an additional constraintgiving rise to the debt-dependent firm value. We solve for theasset value of the firm with debt finance by the use of numericaldynamic programming. This allows us to solve the debt controlproblem and to compute sustainable debt as well as the firm’sdebt value.     

Reduced Form Mortgage Pricing as an Alternative to Option-Pricing Models

This paper extends the traditional hazard technique of estimating prepayment and default by allowing their baselines to be stochastic processes, rather than known paths of time, as is typically assumed. By working in the reduced form, this method offers an alternative to the empirical valuation of mortgages more easily implemented than the standard structural form approach of options pricing.     

Changes in Factor Betas and Risk Premiums Over Varying Market Conditions

We show risk exposures and premiums associated with the Chen, Roll, and Ross (1986) risk factors change over time and depend on stock market and business cycle condition. Findings also indicate that factor risk premiums change sign between January and non-January, especially during bull markets. These findings serve as a caveat for portfolio managers who allocate assets to match desired exposures to key macroeconomic risk factors.     

Signaling-Screening Equilibrium in the Mortgage Market

The signaling model of Spence (1973a) and the screening model of Rothchild and Stiglitz (1976) have been separately used to explain economic phenomena when there is asymmetric information. In the real world, however, situations of asymmetric information often simultaneously involve signaling and screening. In this paper, we combine signaling and screening mechanisms and demonstrate a signaling-screening separating equilibrium. We present the analysis within the framework of mortgage markets. Borrowers signal their default risk types to lenders by acquiring different credit records. This partially separates borrowers into subsets. Lenders screen each subset by offering menus of mortgage loan contracts. Borrowers, then, self-select by choosing particular contracts from the menu. We show the conditions under which the signaling-screening equilibrium is Pareto superior to a screening-only equilibrium.     

The Variation of Economic Risk Premiums in Real Estate Returns

We examine the predictable components of returns on stocks, bonds, and real estate investment trusts (REITs). We employ a multiple-beta asset pricing model and find that there are varying degrees of predictability among stocks, bonds, and REITs. Furthermore, we find that most of the predictability of returns is associated with the economic variables employed in the asset pricing model. The stock market risk premium is highly important in capturing the predictable variation in stock portfolios, and the bond market risk premiums (term and risk structure of interest rates) are important in capturing the predictable variation in bond portfolios. For REITs, however, both the stock and bond market risk premiums capture the predictable variation in returns. REITs have comparable return predictability to stock portfolios. We conclude that there is an important economic risk premium for REITs that are not captured by traditional multiple-beta asset pricing models.     

Determinants of the Dollar Value of Default Risk: A Put Option Perspective

This study uses the option valuation framework to identify andinvestigate the factors affecting the cross-sectional difference inindividual corporate bonds' default risk. The dollar value of defaultrisk (DVDR) is measured by subtracting the observed trading price of arisky corporate bond from a Cox-Ingersoll-Ross model value of acorresponding pseudo-default-free bond. From an option pricingperspective, DVDR can be modeled as the value of a put option on thefirm's risky assets. The DVDR of an individual investment-grade corporatebond is hypothesized to be related to the bond rating, time to maturity ofthe bond, size of the issuing firm, volatility of firm value, and dividendyield of the issuing firm. In the case of the first four factors, theempirical results are consistent with the predictions from a put optionperspective. There is a mixed relationship between DVDR and dividendyield, however, which provides a weaker support for the prediction of theoption valuation model. Such a mixed relationship documents the importantrole that dividend payments play in signaling a firm's future earnings andreducing overall agency costs. ["In particular, the formula can be usedto derive the discount that should be applied to a corporate bond becauseof the possibility of default." (Black and Scholes (1973), Journal of Political Economy, Abstract, p. 637.)]     

我国企业债券违约的特征趋势、融资特点及风险处置机制研究

本文从债券违约的数量规模、行业分布、地域分布、企业属性、债券品种及违约率等方面阐述了我国企业债券违约的特征趋势,分析了我国企业债券违约的主要原因及其所呈现出来的融资特点,探讨了我国企业债券违约后的五种处置方式,认为我国债券违约风险处置机制还不完善,缺少独立法律制度、处置的市场化程度较低、投资者保护机制不健全、对发行人缺乏硬性约束,影响了违约债券的整体兑付水平,投资人利益难以得到有效维护。建议采取多种措施降低债券违约发生率、优化发行人融资结构、建立债券违约的市场化处置机制,以降低债券违约风险,推动债券市场健康发展。     

Gas storage valuation under limited market liquidity: an application in Germany

Natural gas storages may be valued by applying real options theory. However, it is crucial to take into account that most evolving gas markets, like the German spot market, lack liquidity. This implies that large-scale operation of storages reduces the achievable operating margin since storage operators will pay higher prices for injected gas and earn less on withdrawn gas. Optimal storage operation will take this into account. In this context, considering storage operators as price takers does not account for interdependencies of storage operations and market prices. This paper offers a novel approach to storage valuation taking into account the effect of management decisions on market prices. The methodology proposed within this paper determines the optimal production schedule and value by determining the stochastic differential equation describing the storage value and then applying a finite difference scheme. We find that limited liquidity lowers the storage value and reduces withdrawal and injection amounts. Further, we observe decreasing reservation prices for injection and withdrawing for growing illiquidity resulting in a left shift of injection and withdrawing threshold prices.     

债券保险发展进程及业务模式探索

我国信用债市场发展进入新时期,信用违约的常态化和高收益债券市场建立的需要催生了对信用风险管理和信用增级的需求,而债券保险正是满足这两种需求的有效手段。本文在借鉴债券保险发展的国际经验的基础上,立足我国债券市场与债券保险发展现状,指出了当前我国债券保险发展滞后源于制度建设落后、信用保护卖方保障不足等原因导致的盈利困难,并提出和论证了由保险公司提供结算型债券保险的新型保险模式。最后就当前我国债券保险发展存在的不足之处,从发展传统型债券保险和信用风险缓释工具两个角度提出了具体的政策建议。     

房地产贷款中的信息不充分及其风险

房地产市场价格波动之所以能够引起银行房地产信贷损失,甚至导致金融市场和宏观经济不稳定的后果,原因是由于房地产抵押贷款中存在的测不准风险或不确定性。本文从信息不充分的视角,提出了房地产抵押贷款中的测不准风险的定义,并分析了测不准风险的特性、形成原因和特殊后果。本文认为,减少或消除不必要的不可预见和不可描述的不确定性可能是管理房地产抵押贷款违约风险,提高贷款配置效率的最好途径,这对于分析房地产市场价格波动与金融市场、宏观经济的互动关系,防止房地产价格波动对金融业和宏观经济的冲击至关重要。